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In the equation 1/j + 1/k = 1/3 + 1/5, both j and k are positive integers.  What is the sum of all possible values for k?

 May 14, 2021
 #1
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The sum of all possible values of k is 41.

 May 14, 2021
 #2
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The other answer isn't insightful whatsoever.

 

Note RHS = $\frac{8}{15}$ and LHS = $\frac{j+k}{jk}$. So $15j+15k=8jk$. Now use simons favorite factoring trick.

 May 15, 2021

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